Closed form solution of the input impedance of multi-shaped symmetrical quadrilateral loop antenna

The induced EMF method had been used to obtain a closed form solution for open straight thin wires assuming a sinusoidal current distribution. This assumption is true for infinitesimally thin wires. For actual antenna problems, where the wire radius is small but finite, the assumption of sinusoidal current distribution is no longer valid, therefore this method fails especially for antenna lengths near anti-resonance. In an endeavour to overcome the limitation of the EMF method, multi-term sinusoidal current distribution is introduced, where new sinusoidal terms are assumed in addition to the conventional one. The induced EMF method is introduced for first time to get a closed form for the input impedance of closed loops. A symmetrical quadrilateral loop is shown. The wire system of this loop antenna is considered to comprise a number of actual or virtual transmission line subsections, with a characteristic impedance assigned to each subsection.